Solve for unknown variables in proportions (A:B = C:D), simplify ratios to lowest terms, and scale ratios for video aspect ratios, recipes, and monetary budget distributions.
Leave any one field blank (or enter a number in the other three) to solve for the unknown variable.
Ratios express the relative size of two or more values. This calculator lets you solve proportions, simplify integer or decimal ratios, and split totals into proportional shares:
Choose between solving an unknown term in a proportion (A:B = C:D), reducing a ratio to lowest terms, or scaling a ratio against a target total quantity.
Enter your numbers into the active fields. To solve for X in a proportion, leave any one of the four terms blank.
Review the solved variable, simplified integer ratio, part-to-whole percentage allocations, and cross-multiplication proofs.
Video editors and digital artists need to scale resolutions (like 1080p, 1440p, or 4K) while strictly locking 16:9, 4:3, or 21:9 aspect ratios without distortion.
Splitting corporate dividends, bonus pools, or investment contributions among partners in uneven ownership ratios (like 3:5:7).
Mixing concrete (1 part cement : 2 parts sand : 3 parts gravel) or photographic darkroom chemicals requires precise proportional scaling.
Translating blueprint measurements (such as 1 inch = 50 feet) into real-world construction site coordinates.
Switch seamlessly between solving missing variables in proportions, simplifying complex decimal ratios, and distributing totals.
Interactive dual-color bar demonstrates exact percentage shares between terms for intuitive visual comprehension.
Converts messy decimal ratios like 1.25 : 3.75 into clean, canonical integer ratios (1 : 3) automatically.
One-click access to standard media resolutions (16:9, 4:3, 1:1, 21:9, 3:2) for instant workflow acceleration.
A proportion states that two ratios are equivalent. By the fundamental property of proportions, the product of the extremes equals the product of the means:
Solving for an unknown term: \(D = \frac{B \times C}{A}\), \(C = \frac{A \times D}{B}\), \(B = \frac{A \times D}{C}\), or \(A = \frac{B \times C}{D}\).
To calculate part-to-whole percentage shares from a ratio \(A : B\):
Set up the fractional equality and cross-multiply extremes and means:
Sum the ratio parts (3 + 5 = 8), find the value per share, and multiply by each part:
| Aspect Ratio | Standard Resolution | Decimal Factor | Primary Use Case |
|---|---|---|---|
| 16 : 9 | 1920 × 1080 (FHD) | 1.778 | Modern TV, YouTube, Monitors |
| 4 : 3 | 1024 × 768 (XGA) | 1.333 | Classic CRT displays, iPad screens |
| 1 : 1 | 1080 × 1080 (Square) | 1.000 | Instagram square posts, avatars |
| 21 : 9 | 2560 × 1080 (UW-FHD) | 2.333 | Ultrawide gaming, anamorphic cinema |
| 9 : 16 | 1080 × 1920 (Vertical) | 0.5625 | TikTok, Instagram Reels, Shorts |
A ratio compares two parts to each other (part-to-part), while a fraction compares a part to the entire total (part-to-whole). If boys to girls is 3:5, the fraction of boys is 3/(3+5) = 3/8, not 3/5.
When scaling digital assets or masonry mortar mixes, lock your ratio constant to prevent distortion or weak concrete. In concrete work, a standard 1:2:3 volumetric batch requires strict proportion control regardless of container size.
Use the property of cross-multiplication, which states that the product of the extremes equals the product of the means: A * D = B * C. If D is unknown, rearrange the formula to D = (B * C) / A. If C is unknown, C = (A * D) / B. This fundamental rule applies to all linear proportions.
A part-to-part ratio compares two distinct subgroups to each other, such as 3 red marbles to 5 blue marbles (3:5). A part-to-whole ratio compares one subgroup to the total combined collection, such as 3 red marbles out of 8 total marbles (3:8 or 37.5%). You convert a part-to-part ratio A:B into part-to-whole fractions by computing A/(A+B) and B/(A+B).
To simplify a ratio with decimals (such as 1.5 : 2.5), multiply all terms by 10 (or 100) until all values become integers (15 : 25), then divide each number by their Greatest Common Divisor (GCD of 5), yielding 3:5. For fractions like 1/2 : 2/3, multiply both terms by the common denominator 6 to get 3:4.
In a 16:9 aspect ratio, Width / Height = 16 / 9. If you know the width (for example 1920 pixels), height equals (1920 * 9) / 16 = 1080 pixels. If you know the height (720 pixels), width equals (720 * 16) / 9 = 1280 pixels. This same ratio calculation powers all display, photography, and video scaling.
To divide a total amount T into a ratio of A : B, first add the ratio parts together to find the total units: S = A + B. Next, find the value of one single unit by dividing T / S. Finally, multiply this unit value by A and by B respectively to determine the exact allocations.
